Localized deformation such as shear bands, compaction bands, dilation bands, combined shear/compaction or shear/dilation bands, fractures, and joint slippage are commonly found in rocks. Thus, modeling their inception, development and propagation, and effect on stress response is important with regard to making informed engineering design decisions involving these materials. Following a GulfRoc...

We consider the model of interaction between the immune system and tumor cells including a memory function that reflect the influence of the past states, to simulate the time needed by the latter to develop a chemical and cell mediated response to the presence of the tumor. The memory function is called delay kernel. The results are compared with those from other papers, concluding that the mem...

§0 Introduction. In a paper of Wan [W], he proved that for each holomorphic quadratic differential defined on the Euclidean 2-disk, D, there exists a harmonic diffeomorphism from the real hyperbolic plane H R into itself, such that its Hopf differential is the given holomorphic quadratic differential after representing H R by the Poincaré model. In addition, he also proved that this corresponde...

An exact multiplicity result of positive solutions for the boundary value problems u′′ λa t f u 0, t ∈ 0, 1 , u′ 0 0, u 1 0 is achieved, where λ is a positive parameter. Here the function f : 0,∞ → 0,∞ is C2 and satisfies f 0 f s 0, f u > 0 for u ∈ 0, s ∪ s,∞ for some s ∈ 0,∞ . Moreover, f is asymptotically linear and f ′′ can change sign only once. The weight function a : 0, 1 → 0,∞ is C2 and ...

We study local bifurcations of critical periods in the neighborhood of a nondegenerate center of a Liénard system of the form ẋ = −y + F(x), ẏ = g(x), where F(x) and g(x) are polynomials such that deg(g(x)) ≤ 3, g(0) = 0, and g′(0) = 1, F(0) = F ′(0) = 0 and the system always has a center at (0,0). The set of coefficients of F(x) and g(x) is split into two strata denoted by SI and SII and (0,0)...

By constructing a circuit consisting of a diode, resistor, and inductor in series with sinusoidallydriven function generator, period doubling bifurcation and chaotic behavior were observed in this experiment. By using a fixed frequency close to the value of resonance frequency of the circuit and adjusting the voltage amplitude of the function generator, the circuit exhibited chaotic behavior. A...

The modulational instability (MI) of plane waves in nonlocal Kerr media is studied for a general response function. Several generic properties are proven mathematically, with emphasis on how new gain bands are formed through a bifurcation process when the degree of nonlocality, sigma, passes certain bifurcation values and how the bandwidth and maximum of each individual gain band depends on sig...

Two nutrient–phytoplankton–zooplankton (NZP) models for a closed ecosystem that incorporates delay in nutrient recycling, obtained using the gamma distribution function with one or two degrees of freedom, are analysed. The described by systems ordinary differential equations four and five dimensions. purpose this study is to investigate how mean total nutrients affect stability equilibrium solu...